Applications of BWM and GRA for Evaluating the Risk of Picking and Material-Handling Accidents in Warehouse Facilities

Abstract

Warehouse accidents have become of wide concern to the public because they often cause heavy economic losses and heavy casualties. Therefore, it is critical to foster the safety and reliability of warehouse facilities to reduce accidents. However, in the relevant literature, the increased safety of warehouse facilities has seldom been researched. This is a main research gap that the authors would like to supplement with the aim of enhancing warehouse facility reliability to improve risk management in a comprehensive and reliable way. The objectives of this research article are to collect the critical risks from the relevant literature and interviewees, to calculate the weights of four critical indicators (O, S, D, and E) by the BWM approach, and to rank the critical risks of picking and material-handling accidents in a warehouse facility through GRA, the HFACS model, and the FMEA approach. The ranking results show that cost is the most essential element and the expected cost > detection > severity > occurrence, according to the average value of experts’ comprehensive consideration of importance. Next, GRA is used to prioritize the critical risks of picking and material-handling accidents. The main contribution is that we identify 18 major critical risk accidents of the HFACS risk categories and make up for the insufficiency of past research that lacks an empirical analysis of the risks of picking and material-handling accidents in warehouse facilities.

1. Introduction

Accidents have become of wide concern to the public because these accidents not only lead to negative consequences for the physical and mental health of employees, but also to high costs for companies and the entire society [1]. More than $600 billion in direct costs for worker compensation were spent on the most disabling compensable non-fatal injuries and illnesses in the United States from 1998 to 2010 [2]. Due to trade liberalization, commodity flows are promoted, and the relevant warehouse facilities have increased rapidly to enhance the capacities of logistics movement [3]. Because a warehouse provides a building where products and materials are brought in, stored, and later retrieved for shipment to another location [4], the use of forklifts or other powered industrial trucks (PITs) to facilitate the movement and storage of goods grew steadily over the following 10 years [5].

Unfortunately, product movement and storage pose risks to all present in the warehouse facility, especially from forklifts, which are known to be a common source of occupational injuries and fatalities [6]. According to the National Safety Council (NSC), injuries that occur at docks are responsible for 10 to 25% of all workplace injuries. If a tractor prematurely pulls out with a trailer, the lift truck and operator may crash to the dock floor, an accident that could result in heavy injuries/casualties [4]. In addition, according to the U.S. Occupational Safety and Health Administration (OSHA), there are 100,000 accidents reported every year resulting in 95,000 injuries and 100 fatalities, and forklift tip-overs are responsible for 24% of all fatal injuries to operators [4]. Overall, one in every six workplace fatalities are forklift related [6]. Therefore, it is critical to foster the safety and reliability of a warehouse facility on the work floor to reduce the accidents that happen [7].

However, most research focuses on the impact of the perceived safety-related leadership of managers and the worker-safety consciousness concerning the safe behavior of workers. In the relevant literature, effective measures leading to increased safety in a warehouse facility have hardly been researched [8]. From the perspectives of the safety and reliability of warehouse facilities, it must be possible to predict possible problems with the safety of a warehouse facility, to identify and eliminate potential risk factors that could lead to hazards in the future, and to enhance warehouse facility reliability for helping risk managers provide comprehensive and reliable improvements [9].

Besides, human error has been implicated in 70 to 80% of all civil and military aviation accidents. The concept of an HFACS model was developed by James Reason in 1990 [10], developed to meet those needs for improving aviation accident investigations and to reduce the aviation accident rate [11]. The HFACS model also describes the five levels of human negligence, including unsafe behavior, unsafe prerequisite, unsafe supervision, organizational influence, and external factors [12]. The HFACS model has been widely used in the analysis of natural gas pipelines [13], chemical storage [14], etc. Therefore, based on the HFACS model, the five circuital risk categories are used by this article to classify the risks of picking and material-handling accidents in warehouse facilities.

In most cases, several criteria are involved in this identification and selection process, and one of the most-recently developed methods is the best–worst method (BWM). It is a multi-criteria decision-making problem (MCDM) for identifying the weights of the different criteria [15]. It is a comparison-based method that conducts the comparisons in a particularly structured way by which less information is required, and the comparisons are also more consistent [16]. In addition, gray relational analysis (GRA) [17], a normalization evaluation technique, is extended to solve the complicated multi-performance optimization, whose theory is based on the random uncertainty of small samples developed into an evaluation technique to solve certain complex problems [18]. In the field of risk management of reliability and security, failure modes and effects analysis (FMEA) has been an important approach to find the risk priority number (RPN) based on four indicators, which comprise the severity of the failure effect (S), the probability of occurrence of the failure mode (O), the probability of failure detection (D), and the expected cost (E) [19].

As noted previously, based on the HFACS model and FMEA approach, the BWM and GRA are the important MCDM methods, which are used by this article to calculate quantitative RPN research for evaluating the risk of picking and material-handling accidents in warehouse facilities. The objectives of this research are as follows:

• To collect the critical risks of picking and material-handling accidents in the ware-house facility by the relevant literature and interviewees of a case study,
• To classify the critical risks based on the HFACS model of five levels of human negligence,
• To calculate the weights of four critical indicators (O, S, D, and EC) by the BWM approach, and
• To rank the critical risks of picking and material-handling accidents in a warehouse facility through GRA for providing decision-makers with a reference.

This research article comprises six sections. Apart from the introduction in section one, the second section reviews the theoretical literature, the third section explains the research methods, the fourth section presents the results, the fifth section is further discussions, and the last section provides conclusions to this research article.

2. Theoretical Literature

The main objective of this research study is to explore the critical risks of picking and material-handling accidents in warehouse facilities to provide decision-makers with risk mitigation. The model [19] of the human factors analysis and classification system (HFACS) and failure mode and effects analysis (FMEA) are directly cited by this paper for the purpose. This section is divided into three parts. Section 2.1 illustrates that HFACS is a proper model for risk evaluation and can be used by this paper to identify the critical risks of picking and material-handling accidents through the relevant literature. Section 2.2 presents the FMEA measurements of the importance of related risk indicators. Section 2.3 reviews the relevant literature of the logistics of warehouse facility safety.

2.1. Human Factors Analysis and Classification System (HFACS)

Human error has been implicated in 70 to 80% of all civil and military aviation accidents. The concept of the HFACS model was developed by James Reason in 1990 [10] and was generally referred to as the “Swiss cheese” model of human error, describing five levels of human failure, each influencing the next [11]. To identify the human causes of an accident, the HFACS model was developed to meet the need to offer analyzing tools as a way to plan preventive training. In addition, it is an important taxonomic nature and can be easily applied in practical application [20]. Therefore, it has been used within the military, commercial, and general aviation sectors for reducing the accidents that happen, including to systematically examine underlying human causal factors and to improve aviation accident investigations [11].

In addition, the HFACS model of accident investigations is also an important qualitative approach to understanding and managing facility safety that is used by some government departments, such as the United States Coast Guard and the US Department of Defense [18]. To better understand the potential safe implications for avoiding the risks of picking and material-handling accidents in a warehouse facility [21], the HFACS model is used by this article and is described in detail as follows, including the five levels of human negligence [11,20,21]:

• Unsafe behavior (UB): this can be classified into two categories, including errors and violations. Errors represent the mental or physical activities of individuals that fail to achieve their intended outcome, which dominate most accident databases, including three basic error types of skill-based, decision, and perception. Violations refer to the willful disregard for the rules and regulations that govern the safety of flight, including two violating forms of routine and exception.
• Precondition for unsafe behavior (PUB): this can be classified into two major conditions, including substandard conditions of operators (adverse mental states, adverse physiological states, and physical/mental limitations) and the substandard practices they commit (crew resource mismanagement and personal readiness).
• Unsafe supervision (US): the causal chain of events is traced to back up the supervisory chain of command. Four categories of unsafe supervision have been identified, including inadequate supervision, planned inappropriate operations, failure to correct a known problem, and supervisory violations. For example, there is inadequate on-the-job training and inadequate train-the-trainer training.
• Organizational influence (OI): this can be classified into three categories, including the organizational process, resource management, and organizational climate. For example, fallible decisions of upper-level management directly affect supervisory practices, as well as the conditions and actions of operators.
• External environment factors (EEF): it can be the technological environment or the physical environment. The technological environment refers to a broken wire, an improperly installed cable, or a failure of the automated pullback protection system. The physical environment is, for example, working in inadequate lighting of the yard or flying in severe blizzard weather.

2.2. Failure Mode and Effects Analysis (FMEA)

MEA is a tool widely used in the automotive, aerospace, and electronics industries that is often used to identify, prioritize, and eliminate known potential failures, problems, and errors in a process or product. In FMEA, the potential failure modes and their effects are brainstormed, including the severity of the effect of the failure mode, the occurrence of the failure mode, the detection of the failure mode, and the expected cost, which is to be scaled from 1 to 10 [22]. Therefore, a larger set of empirically derived failures are collected, and unanticipated failures are identified [23]. In addition, FMEA is also a risk management technique, whose purpose can be to prioritize potential failures in accordance with their “risk”. The prioritized risks enable risk managers to eliminate or reduce the occasions of possible failures, problems, and errors [19]. There are often four risk indicators, which are described in detail as follows [19,22,23]:

• Occurrence (O)—how likely is the failure cause to occur in the risk calculations? It is crucial to evaluate the probability of occurrence, the probability of the cause and immediate failure mode, and the probability of the cause event and end effects. However, the result could be different from the probability of the end effects in the failure mode. The occurrence is estimated using a 1–10 scale.
• Severity (S)—refers to a severity of effect, which is used to measure the seriousness of the effects of a failure mode, as well as to describe how serious the end effects of the failure mode are. The severity categories are estimated using a 1–10 scale; for example, 10 is defined as “total lack of function”, 5 is “moderate degradation in performance”, and 1 is “effect almost no noticeable”.
• Detection (D)—refers to a difficulty of detection, which describes how likely the failure mode is to be detected. There are several definitions for detection, which generally fall into one of the following categories: (1) detection during the design and development process; (2) detection during the manufacturing process; and (3) detection during operation. These detection scores are based on that the lower the 1–10 detection score is, the better the detection capability.
• Expected cost (EC)—as a measure of risk, it explains how risk contains two basic elements: chance and consequence. Probability is a universal measure of chance, and cost is an accepted measure of consequences. Given a failure scenario, risk can be calculated as a failure or expected cost. In fact, the expected cost is widely used in the fields of risk analysis, economics, decision theory, etc. Both probability and cost are ratio scales, which are estimated by using a 1–10 scale.

2.3. Warehouse Facility Safety

A warehouse is considered an important structured logistics system, which is strongly associated with dynamic process execution such as receiving, storing, picking, issuing, warehousing, etc. [24]. In the past, warehouses were referred to as cost centers and rarely added value, but now, the increasing need to transfer products across cities, countries, and continents results from the movement of production to the Far East. In addition, the growth in e-commerce and increasing demands from end-users enable business enterprises to change their perceptions of warehouses. Because warehouses are likely involved in various stages of sourcing, production, temporary storage, ordering, and distribution of goods, as well as the handling of raw materials and works in progress through to finished products, as shown in

Table 1. Picking and materials handling in the warehouse facility [25].

No.	Function	Description
1	Receiving	This is the process of unloading an incoming truck, identifying, registering, and sometimes repacking.
2	Put away	This happens when goods are moved from the unloading dock to the storage area.
3	Storage, in and out	Activities at the warehouse affect the goods in storage: to count and verify inventory quantities.
4	Replenishment	If inventory levels of the pick storage drop to certain amounts, it is replenished with stocks from the bulk storage.
5	Pick and pack	Upon an order for a needed item in storage, either full pallets are picked from the bulk area of storage, or smaller quantities are picked from the pick area of storage.
6	Shipping	The picked items are packed, consolidated, and staged for shipping.
7	Cross-dock	Some goods do not make their way into stocks but, upon receipt, are transferred to the shipping dock for shipment to point of need.
8	Value-added service	There is also recognition for the value added at distribution centers. Such value can be the labeling of goods to the specific customer or the country of destination.

, all effects on the warehousing roles are therefore required to perform under the current situation of increasing market volatility, product range proliferation, shortening lead times, etc. [25].

Besides, a warehouse is a building with many dock doors around the various sides for the purpose of picking and materials handling. The focus is on the internal transportation of goods from point of receipt to storage and to the dispatch area, and vice versa. It is apparent that different types of equipment are needed to move and store items [26]. Transport equipment usually offers many benefits such as improving the efficiency of working or reducing the need for manual handling. As a result, they often pose major opportunities for occupational hazards [25].

In fact, the place of warehousing equipment has been considered a fast-paced/high-risk workplace of operations. By nature, the place often leads to injuries and the safety of personnel should be highlighted. Therefore, when the requirement is used for the easy and efficient carriage of goods from one point to another in the warehouse facility, it is very crucial to the working staff for reducing the risks and providing safer operations of docks, powered industrial trucks, conveyors, materials storage, manual lifting/handling, and charging stations [4]. There are seven possible warehouse incidents that include inbound put-away, warehousing inventory move, warehousing move order issue, outbound picking, warehousing counting, inbound receiving, and outbound staging move [26].

To sum up, with regard to warehouse facility safety, most research focuses on the impact of the perceived safety-related leadership of managers and worker safety consciousness. In the relevant literature [4,5,6,7,8,24,25,26], effective measures for picking and material-handling accidents leading to decreased risk in a warehouse facility for heavy injuries/casualties have hardly been researched. This is the main aspect, or research gap, that the authors would like to supplement in this paper with the aim of evaluating the risk of picking and material-handling accidents for decreasing heavy injuries/casualties in a logistics warehouse facility.

3. Methods

The main objective of this research is to collect/classify/rank critical risks of picking and material-handling accidents in a warehouse facility, providing decision-makers with references. The best–worst method (BWM) and grey relational analysis (GRA) are directly cited by this paper for this purpose. This section is divided into two parts, which separately present the BWM and GRA calculation processes of the mathematical step, including to explain their applicability to this research study.

3.1. Best–Worst Method (BWM)

A new method [27], called best–worst method (BWM) is a multi-criteria decision-making method that uses two vectors of pairwise comparisons to determine the weights of criteria. BWM has been significantly ranked in the field of MCDM as a model providing reliable and relevant results for optimal decision-making [28]. It compares to the existing MCDM methods, as described below: (1) it requires less comparison data; and (2) it leads to more consistent comparisons, which means that it produces more reliable results [27]. First, the best (e.g., most desirable, most important), and the worst (e.g., least desirable, least important) criteria are identified by the decision-maker, after which the best criterion is compared to the other criteria, and the other criteria to the worst criterion.

In addition, a nonlinear minimax model is then used to identify the weights so that the maximum absolute difference between the weight ratios and their corresponding comparisons is minimized [16]. Furthermore, the grey values represent the information as an interval for which the linguistic terms for pairwise comparison of RPN elements is shown in

Table 2. Linguistic terms for pairwise comparison of RPN elements [19].

No.	Linguistic Variables	Codes	Interval Value
1	Equally important	E	[1, 2]
2	Moderately important	M	[2, 4]
3	Strongly important	S	[4, 6]
4	Very strongly important	VS	[6, 8]
5	Extremely important	EX	[8, 9]

. The steps of BMW are used to derive the weights of the criteria, which are briefly described as follows [19]:

Step 1.

Determine a set of RPN elements

The expert identifies n RPN elements (e.g., frequency and severity) that are used to calculate the RPN values.

Step 2.

Determine the best and worst RPN elements

The expert selects the best (i.e., most acceptable, preferred, or vital) and worst (i.e., least acceptable, preferred, or vital) RPN elements from the n RPN elements determined in Step 1.

Step 3.

Determine the preference of the best RPN element over the other RPN elements

The expert assigns the preference of the best RPN element over the other RPN elements on a ranking scale of 1 (least important) to 9 (most important). The resulting best-to-others (BO) vector is:

$$A_B=\left(a_{B1},a_{B2},\cdots ,a_{Bn}\right)$$

where $a_{Bj}$ is the preference of the best element B over element j. Clearly, $a_{BB}$ = 1.

Step 4.

Determine the preference of the other RPN elements over the worst RPN element

The relative importance of the other RPN elements over the worst RPN element is assigned by the expert on a ranking scale of 1–9. The resulting others-to-worst (OW) vector is:

$$A_W={\left(a_{1W},a_{2W},\cdots ,a_{nW}\right)}^T$$

where $a_{jW}$ is the preference of the element j over the worst RPN element w. Clearly, $a_{WW}$ = 1.

Step 5.

Determine the optimal weights: $\left(w_1^{*},w_2^{*},\cdots ,w_n^{*}\right)$

The optimal weights of the RPN element are determined such that the maximum absolute differences $\left|w_B-a_{Bj}\times w_j\right|$ and $\left|w_j-a_{jW}\times w_W\right|$ for all j are minimized, which is translated to the following min–max model:

$${\min }_j\max \left\{\left|w_B-a_{Bj}\times w_j\right|,\left|w_j-a_{jW}\times w_W\right|\right\}$$

$$\begin{array}{l}\mathrm{\text{Subject to}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \sum _j{w}_j}=1, w_j\ge 0, \mathrm{\text{for all}} \mathit{j}\end{array}$$

(1)

This can be converted into the following linear programming formulation to solve:

min Z;

$$\begin{array}{l}\mathrm{\text{Subject to}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left|w_B-a_{Bj}\times w_j\right|\le Z, \mathrm{\text{for all}} \mathit{j}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left|w_j-a_{jw}\times w_w\right|\le Z, \mathrm{\text{for all}} \mathit{j}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \sum _j{w}_j}=1, w_j\ge 0, \mathrm{\text{for all}} \mathit{j}\end{array}$$

(2)

After the expert answers the pairwise comparisons, we can obtain the BO and OW with a total of two grey vectors, which are illustrated as follows:

$$\begin{array}{l}{\tilde{A}}_B=\left({\tilde{a}}_{B1},{\tilde{a}}_{B2},\cdots ,{\tilde{a}}_{Bn}\right)\\ {\tilde{A}}_W=\left({\tilde{a}}_{1W},{\tilde{a}}_{2W},\cdots ,{\tilde{a}}_{nW}\right)\end{array}$$

Therefore, the constrained optimization problem for determining the optimal interval weights ${\tilde{w}}_1^{*}=\left({\tilde{w}}_1^{*},{\tilde{w}}_2^{*},\cdots ,{\tilde{w}}_n^{*}\right)$ can be obtained as follows:

$\min {\tilde{Z}}^{*};$

$$\begin{array}{l}\left|\left(w_B^l,w_B^u\right)-\left(w_j^l,w_j^u\right)\times \left(w_{Bj}^l,w_{Bj}^u\right)\right|\le \left(Z^{*},Z^{*}\right), \mathrm{for} \mathrm{all} j\\ \left|\left(w_j^l,w_j^u\right)-\left(w_W^l,w_W^u\right)\times \left(w_{jW}^l,w_{jW}^u\right)\right|\le \left(Z^{*},Z^{*}\right), \mathrm{for} \mathrm{all} j\\ {\displaystyle \sum _{j=1}^{n}R\left({\tilde{w}}_j\right)=1;} w_j^l\le w_j^u; w_j^l\ge 0, \mathrm{for} \mathrm{all} j\end{array}$$

(3)

$\mathrm{where} {\tilde{w}}_B=\left(w_B^l,w_B^u\right),{\tilde{w}}_j=\left(w_j^l,w_j^u\right),{\tilde{w}}_W=\left(w_W^l,w_W^u\right),{\tilde{a}}_{Bj}=\left(a_{Bj}^l,a_{Bj}^u\right),{\tilde{a}}_{jW}=\left(a_{jW}^l,a_{jW}^u\right)$ and suppose ${\tilde{Z}}^{*}=\left(Z^{*},Z^{*}\right)$. They are the interval values that replace the crisp value. An application of the calculation by this article is in Section 4.

3.2. Grey Relational Analysis (GRA)

The grey system theory (GST) has been considered as a better method for doing research on an exploratory explanation. GRA is the most important topic in GST, whose main function is the measurement between two discrete sequences. GRA makes use of relatively simple mathematical procedures and a small amount of data and works with a great variability in factors to arrive at salient relationships in a complex system [29]. Hence, GRA is chosen as the mathematical core to analyze the state of ranking the critical risks of picking and material-handling accidents in warehouse facilities.

A Likert scale involved in research usually uses a 5, 7, or 9-point scale to respond to subjective or objective evaluation. GRA is an important weight analysis method that is weighted on a 5-point scale by this article to respond to relative importance evaluation, as shown in

Table 3. The scale for the weighted elements [29].

No.	Linguistic Variables	Codes	Grey Numbers
1	Very poor	VG	[1,2]
2	Poor	P	[2,4]
3	Strongly important	M	[4,6]
4	Good	G	[6,8]
5	Very good	VG	[8,9]

. The obtained data are usually expressed as the specific range of a grey interval number and are the upper and lower limits of the information separately. GRA-associated equations are described as follows [17,18].

Step 1.

Identify the response variables

A normalization of the response variables was performed to prepare raw data for analysis where the original sequence is transferred to a comparable sequence. The process of linear normalization of the original sequence is a larger-the-better characteristic, which is used to normalize the original sequence using the following equation:

$$x_j(k)=\frac{x_j{}^{(0)}(k)-\min x_j{}^{(0)}(k)}{\max x_j{}^{(0)}(k)-\min x_j{}^{(0)}(k)}$$

(4)

For the smaller-the-better (undercut) quality characteristic of the original reference sequence, the following expressions are used for normalization:

$$x_i{}^{*}(k)=\frac{\max x_i{}^{(0)}(k)-x_i{}^{(0)}(k)}{\max x_i{}^{(0)}(k)-\min x_i{}^{(0)}(k)}$$

(5)

Step 2.

Determination of Deviation Sequences

The deviation sequence ${\Delta }_{0i}(k)$ is the absolute difference between the reference sequence $x_0{}^{*}(k)$ and the comparability sequence $x_i{}^{*}(k)$ after normalization. The value of $x_0{}^{*}(k)$ is considered as 1. It is determined using Equation (6) as given below:

$${\Delta }_{0i}(k)=\left|x_0{}^{*}(k)-x_i{}^{*}(k)\right|$$

(6)

Step 3.

Calculation of Grey Relational Coefficient (GRC)

Grey relational coefficients for all the sequences express the relationship between the ideal and actual normalized response variables. The grey relational coefficient $\gamma (x_0(k),x_i(k))$ can be expressed by Equation (7):

$$\gamma (x_0(k),x_i(k))=\frac{\Delta \min +\xi \Delta max}{{\Delta }_{0i}(k)+\xi \Delta max}$$

(7)

where Δ min is the smallest value of ${\Delta }_{0i}(k)$ = min $\left|x_0{}^{*}(k)-x_i{}^{*}(k)\right|$ and Δ max is the largest value of ${\Delta }_{0i}(k)$ = max $\left|x_0{}^{*}(k)-x_i{}^{*}(k)\right|$, $x_0{}^{*}(k)$ is the ideal normalized values, $x_i{}^{*}(k)$ is the normalized comparability sequence, and ξ is the distinguishing coefficient. The value of (ξ) is taken as 0.5 for all response variables and is substituted in Equation (7). The gray relational grade for all the experimental runs were calculated.

Step 4.

Determination of Grey Relational Grade (GRG)

Based on the different weights of BWM calculation, the grey relational grade is a sum of the grey relational coefficient, which is defined as follows:

$$\gamma (x_0,x_i)={\displaystyle \sum _{i=1}^m{W}_i*(}{x}_0(k),x_i(k))$$

(8)

where $\gamma (x_0,x_i)$ is the grey relational grade for the jth experiment.

4. Results

Based on the objectives of this research described in the introduction section, the results are as follows: the first objective is based on the HFACS model to collect critical risks of picking and material-handling accidents in warehouse facilities from the relevant literature and interviewees of a case study. The result of the critical risks is shown in Section 4.1. In addition, the other objective is to calculate the weights of four critical indicators by the BWM approach, and the result of calculating the weights of critical risks is shown in Section 4.2. The last objective is to rank the critical risks of picking and material-handling accidents in the warehouse facility through GRA to provide decision-makers with references, and the result of ranking the critical risks is shown in Section 4.3. Besides, the management implications are presented in Section 4.4.

4.1. Collecting the Critical Risks

This study established a four-person decision-making group to explore the critical risks of picking and material-handling accidents in warehouse facilities, which include two published authors from academic areas, specialists in logistics, and two invited experts from logistics industrial areas to serve as research committee members, including Ming-Hon Hwang, Hsin-Yao Hsu, Zhang Jiyu, and Po-Heng Tsou. The objective of this risk evaluation is to collect and identify potential failures for providing decision-makers with references. Therefore, the process of this article is first to collect the critical risks of picking and material-handling accidents in the warehouse facility through interviewees of a case study and the relevant literature reviews.

The professional interviewee, Zhang Jiyu of the PX Mart Guanyin Logistics Center, was invited to participate in this study for collecting the critical risks of picking and material-handling accidents. Zhang is a site manager and in the beginning of interviewing him he agreed to have his name published. He is responsible for the storage and distribution of goods sold in 500 supermarkets in northern Taiwan, including the operation management of logistics centers and professional distribution services for normal- and low-temperature products.

In addition, Po-Heng Tsou is currently CEO of the Global Logistics and Commerce Council of Taiwan, where he is mainly in charge of planning, matching, training, consultation, cross-border e-Commerce, etc. In the meantime, Philip Tsou acts as the CEO of SOLE-The International Society of Logistics Taiwan (Taipei) Chapter, an important logistics education and research institution of which the goals are to enhance technology management, education, humanities, and social sciences in logistics, and particularly the promotion of international logistics certification.

Determinants of the critical risks of picking and material-handling accidents in the warehouse facility by interviewees are based on the following selected issues of the HFACS model study:

• Question 1. What are common injuries in the warehouse facility when you process picking and materials handling?
• Question 2. With regard to the injuries from unsafe behavior, what is identified as the precondition for unsafe behaviors?
• Question 3. Before this injury occurred, was the reason unsafe supervision from your supervisor, such as inadequate supervision, planned inappropriate operations, or failure to correct a known problem for you?
• Question 4. With regard to the occurred injury, what were the fallible decisions of upper-level management that directly affected the supervisory risk practices in the ware-house facility? For example, excessive cost cutting leads to deficient training.
• Question 5. What external environmental factors were the main cause of the injury occurrence? For example, because of interactions with the improper manning under a surge in orders, did an overexertion injury happen to staff working at picking and materials handling in the warehouse facility?

The collected critical risks of picking and material-handling accidents in the warehouse facility were also amended by the relevant literature. The brainstorming sessions were held for classifying/adding/removing the results. After three discussions and revisions, 18 critical risks of picking and material-handling accidents in the warehouse facility were integrated into this article for the research purposes, as shown in

Table 4. Risks of picking and material-handling accidents by relevant literature and interviewees.

No.	Failure	Description
F1	Overexertion	The physical injuries from excessive lifting, pushing, pulling, holding, carrying, and throwing may be involved under the situation of improper manning because of a recent a surge in orders in the logistics center.
F2	Repetitive motion	Pain is imposed by stress upon some part of the body because of a task’s repetitive nature, which often gets better on its own. The injury most often affects the shoulders, elbows, forearms and wrists, and hands and fingers during the work of warehousing.
F3	Bodily reaction	Injuries are forced by strain upon some part of the body, such as bending, climbing, reaching, standing, sitting, slipping, tripping, or falling down. They may be due to hazards produced by improper storage and reaching for picking things without stable footing in the workplace.
F4	Fall on same level	Inevitably, while walking or climbing up and down in the workplace of a warehouse, injuries from foot slippage and loss of equilibrium may frequently occur in the condition of the soles stained with oil, frost, and mud.
F5	Fall to lower level	The impacted force of falling from a height is generated by gravity, which often leads to significant injuries such as fractures. The accidents of tripping, falling, and emptying are caused most often by uneven workplaces in warehouses, such as covering tarpaulins on the uneven surface of goods.
F6	Struck by object	In the warehouse, the injuries produced by forcible contact with cargo/equipment is often under a cargo-collapse situation when the cargo is rods or tubular goods (such as square wood, round wood, PVC pipe, etc.). The foot-jammed injury easily occurs while you are walking on this surface of goods.
F7	Struck against object	Injury is produced by forcibly colliding into an object, such as a worker walking into a door. The injury can be actively hitting an object, which more often occurs in warehouse areas while the forklift or powered facility is being manipulated and moved.
F8	Struck by protrusion	Worker injures himself by colliding with the protrusions of hooks, beams, side rails, or loading cargo while he is loading/unloading and walking next to the vehicle.
F9	Object falling	The cargo might fall on a worker from above and cause damage to personnel and equipment while the workers are carrying out picking and material handling but are negligent about fixing the roll tie.
F10	Wrapped/clamped	While handling facilities, conveyor belts, or power equipment are moving in the warehouse area, the facilities sometimes cause clothing to be clamped, as well as wrapped injuries to hands or feet.
F11	Caught in or compressed by	A part of a person is injured by being squeezed, crushed, pinched or compressed. The injury occurrences are due to inevitably entering into some narrower roadways for the loading and unloading of goods in the warehouse area. For example, the accident of scratches and crush injuries to the head easily take place after the driver sticks his own head out the window.
F12	Highway incident	This refers to accidents to the powered facility/forklift/vehicle occupant. The struck/attacked injuries occur frequently in the areas surrounding the warehouse, such as the street, road, shoulder, telephone poles, trees aligning roadway, etc.
F13	Tool rebound/bump	This refers to the injuries from an auxiliary tool rebound or bump. For example, the worker is using implements or rope/seatbelt tensioners to load and tighten cargo. Accidentally, the incidents take place by the tool slipping off, or the straps and hooks suddenly fracturing and hitting the worker.
F14	Electric shock	While the worker is conducting power-on, packaging, maintenance, handling, or operating equipment, accidents involving electric shocks more often occur because of static electricity, damp ground, or ground-wire damage. Equally important, while walking on high places, the person should pay more attention to keep his head from accidentally touching wires.
F15	Burn by high/ low temperature	Burn injuries occur frequently in a warehouse’s areas of operation from low-temperature equipment such as refrigerated warehouses and freezers, as well as from high-temperature equipment such as car-cooling radiators, exhaust pipes, engines, and battery terminals.
F16	Hazardous materials	The operational activities of some distribution processing might be hazardous to your health. Injuries come from the value-added activities in warehousing because of being in touch with coating and painting material, PVC shrinkable film package, dispersion, or solvent processing.
F17	Unsafe distance	Injuries are from the unsafe distances among those cooperating with mechanical work. For example, a worker enters the working range of a crane during the hoisting process, and accidents involving hanging objects falling sometimes happens.
F18	Assault/violent	The warehousing worker is injured by a person by intentional assaults, violent acts, and harmful actions. For example, after a quarrel with his colleagues or supervisor, injuries from an assault or other violent crime take place in the warehousing workplace.

.

4.2. Calculating Weight of FMEA Items

The levels of influence of the RPN elements (O, S, D, and EC) usually differ for many practical applications. Thus, the different weighted elements will affect subsequent risk evaluation. The purpose of this research article is to evaluate the risks of picking and material-handling accidents in warehouse facilities; therefore, an empirical case focused on Taiwan’s Logistics Center is selected by this paper. Then the proposed BWM model [19] is used to calculate the proper weights of RPN elements for offering risk evaluation in the next stage, the calculation steps of which are explained in Section 2.1, and Equations (1)–(3) are used for calculating weights.

The information of the data collected from eight specialists is shown in

Table 5. Importance of the best criterion over all the criteria.

	Best	Occurrence	Severity	Detection	Expected Cost
Expert 1	Expected cost	M	S	M	E
Expert 2	Expected cost	S	VS	M	E
Expert 3	Detection	VS	S	E	M
Expert 4	Expected cost	VS	S	M	E
Expert 5	Severity	VS	E	S	M
Expert 6	Severity	VS	E	M	S
Expert 7	Expected cost	S	VS	M	E
Expert 8	Detection	VS	M	E	S

and

Table 6. Importance of the worst criterion over all the criteria.

	Exp. 1	Exp. 2	Exp. 3	Exp. 4	Exp. 5	Exp. 6	Exp. 7	Exp. 8
Worst	Sev.	Sev.	Sev.	Occu.	Occu.	Occu.	Sev.	Occu.
Occurrence	M	M	E	E	E	E	M	E
Severity	E	E	M	M	VS	VS	E	S
Detection	M	S	VS	S	M	S	S	VS
Expected cost	S	VS	S	VS	S	M	VS	M

. The interviewees, whose work experiences in the involved professions are all over 10 years, are working in relative logistics or the PX Mart Guanyin Logistics Center. Their background information is detailed in

Table A1. Work and educational backgrounds of eight experts.

No.	Working	Years of Experience	Education
Expert 1	Related logistics	11	Ph.D.
Expert 2	PX Mart Logistics center	15	Bachelor
Expert 3	Logistics institutions	23	Master
Expert 4	PX Mart Logistics center	25	Bachelor
Expert 5	PX Mart Logistics center	25	college
Expert 6	Logistics transportation	15	Bachelor
Expert 7	PX Mart Logistics center	15	Bachelor
Expert 8	PX Mart Logistics center	17	Bachelor

. In the logistics industry, the experts evaluated the impact scores given in each case on the basis of Table 2 and considered the information uncertainty to ensure that the analysis reflected the real-world situation.

The calculation process of the mathematical steps is described in detail in

Table A2. Weights of the RPN element calculated by LINGO 19.0.

Expert 1	Expert 2
min = z; ! Subject to @abs(wl4-2*wu1)<=z; @abs(wl4-4*wu2)<=z; @abs(wl4-2*wu3)<=z; @abs(wl1-2*wu2)<=z; @abs(wl3-2*wu2)<=z; @abs(wu4-4*wl1)<=z; @abs(wu4-6*wl2)<=z; @abs(wu4-4*wl3)<=z; @abs(wu1-4*wl2)<=z; @abs(wu3-4*wl2)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/3.0;	min = z; ! Subject to @abs(wl4-4*wu1)<=z; @abs(wl4-6*wu2)<=z; @abs(wl4-2*wu3)<=z; @abs(wl1-2*wu2)<=z; @abs(wl3-4*wu2)<=z; @abs(wu4-6*wl1)<=z; @abs(wu4-8*wl2)<=z; @abs(wu4-4*wl3)<=z; @abs(wu1-4*wl2)<=z; @abs(wu3-6*wl2)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/4.47;
Expert 3	Expert 4
min = z; ! Subject to @abs(wl3-6*wu1)<=z; @abs(wl3-4*wu2)<=z; @abs(wl3-2*wu4)<=z; @abs(wl2-2*wu1)<=z; @abs(wl4-4*wu1)<=z; @abs(wu3-8*wl1)<=z; @abs(wu3-6*wl2)<=z; @abs(wu3-4*wl4)<=z; @abs(wu2-4*wl1)<=z; @abs(wu4-6*wl1)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/4.47;	min = z; ! Subject to @abs(wl4-6*wu1)<=z; @abs(wl4-4*wu2)<=z; @abs(wl4-2*wu3)<=z; @abs(wl2-2*wu1)<=z; @abs(wl3-4*wu1)<=z; @abs(wu4-8*wl1)<=z; @abs(wu4-6*wl2)<=z; @abs(wu4-4*wl3)<=z; @abs(wu2-4*wl1)<=z; @abs(wu3-6*wl1)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/4.47;
Expert 5	Expert 6
min = z; ! Subject to @abs(wl2-6*wu1)<=z; @abs(wl2-4*wu3)<=z; @abs(wl2-2*wu4)<=z; @abs(wl3-2*wu1)<=z; @abs(wl4-4*wu1)<=z; @abs(wu2-8*wl1)<=z; @abs(wu2-6*wl3)<=z; @abs(wu2-4*wl4)<=z; @abs(wu3-4*wl1)<=z; @abs(wu4-6*wl1)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/4.47;	min = z; ! Subject to @abs(wl2-6*wu1)<=z; @abs(wl2-2*wu3)<=z; @abs(wl2-4*wu4)<=z; @abs(wl3-4*wu1)<=z; @abs(wl4-2*wu1)<=z; @abs(wu2-8*wl1)<=z; @abs(wu2-4*wl3)<=z; @abs(wu2-6*wl4)<=z; @abs(wu3-6*wl1)<=z; @abs(wu4-4*wl1)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/4.47;
Expert 7	Expert 8
min = z; ! Subject to @abs(wl4-4*wu1)<=z; @abs(wl4-6*wu2)<=z; @abs(wl4-2*wu3)<=z; @abs(wl1-2*wu2)<=z; @abs(wl3-4*wu2)<=z; @abs(wu4-6*wl1)<=z; @abs(wu4-8*wl2)<=z; @abs(wu4-4*wl3)<=z; @abs(wu1-4*wl2)<=z; @abs(wu3-6*wl2)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/4.47;	min = z; ! Subject to @abs(wl3-6*wu1)<=z; @abs(wl3-2*wu2)<=z; @abs(wl3-4*wu4)<=z; @abs(wl2-4*wu1)<=z; @abs(wl4-2*wu1)<=z; @abs(wu3-8*wl1)<=z; @abs(wu3-4*wl2)<=z; @abs(wu3-6*wl4)<=z; @abs(wu2-6*wl1)<=z; @abs(wu4-4*wl1)<=z; (wl1 + wu1 + wl2 + wu2 + wl3 + wu3 + wl4 + wu4)/2 = 1; wl1 >= 0; wl2 >= 0; wl3 >= 0; wl4 >= 0; wu1 >= 0; wu2 >= 0; wu3 >= 0; wu4 >= 0; wl1 <= wu1; wl2 <= wu2; wl3 <= wu3; wl4 <= wu4; CR = z/4.47;

LINGO, a modeling software, is designed to make building and solving mathematical optimization models. Available online: https://www.lindo.com/lindoforms/downlingo.html (accessed on 27 November 2022).

. In addition, the results of the various weighted RPN elements (O, S, D, and EC) are shown in

Table 7. Weights of the RPN elements (O, S, D, and EC).

	Expert 1		Expert 2		Expert 3		Expert 4		Expert 5
	L	U	L	U	L	U	L	U	L	U
${\tilde{w}}_O$	0.148	0.261	0.117	0.153	0.063	0.069	0.063	0.069	0.063	0.069
${\tilde{w}}_S$	0.080	0.102	0.063	0.069	0.117	0.153	0.117	0.153	0.512	0.604
${\tilde{w}}_D$	0.148	0.261	0.176	0.306	0.512	0.604	0.176	0.306	0.117	0.153
${\tilde{w}}_{EC}$	0.466	0.534	0.512	0.604	0.176	0.306	0.512	0.604	0.176	0.306
	Expert 6		Expert 7		Expert 8		Interval Weight
	L	U	L	U	L	U	L	U	Average	Rank
${\tilde{w}}_O$	0.063	0.069	0.117	0.153	0.063	0.069	0.087	0.114	0.101	4
${\tilde{w}}_S$	0.512	0.604	0.063	0.069	0.176	0.306	0.205	0.257	0.231	3
${\tilde{w}}_D$	0.176	0.306	0.176	0.306	0.512	0.604	0.249	0.356	0.302	2
${\tilde{w}}_{EC}$	0.117	0.153	0.512	0.604	0.117	0.153	0.324	0.408	0.366	1

. The results of the interval weights are shown as follows:

$${\tilde{w}}_O=[0.087, 0.114], {\tilde{w}}_S=[0.205, 0.257], {\tilde{w}}_D=[0.249, 0.356], {\tilde{w}}_{EC}=[0.324, 0.408]$$

The result shows that the expected cost is the most important element, as well as the expected cost > detection > severity > occurrence, according to the average value of the experts’ comprehensive consideration of importance.

4.3. Ranking the Failure Modes

Based on the FMEA risk-evaluation approach, this study uses the following questions to assist logistics managers in making appropriate evaluations of the risks of picking and material-handling accidents in the warehouse facility. Determinants are based on the selected questions below:

• Question 1: What is the severity of the injury to the people after the failure mode occurs?
• Question 2: What is the probability of the failure mode occurring?
• Question 3: How easy is it to detect the failure mode before an occupational hazard?
• Question 4: What are the associated costs for worker compensation with the failure mode occurring?

The average scores derived from the risk evaluation surveys of the eight experts are shown in Table 7. Because the interval weights of the RPM elements were determined, the interval concept with BWM is used to improve the information uncertainty. The interval concept with GRA is also used by this paper to obtain the priority for each failure mode, as shown in Table 3. The calculation steps are explained in Section 3.2, and Equations (4)–(8) are used for ranking.

Table 8. Assessment matrix of average score of the eight experts.

	O-L	S-L	D-L	EC-L	O-U	S-U	D-U	EC-U
wi	0.044	0.103	0.125	0.162	0.057	0.129	0.178	0.204
F1	6.000	3.375	7.000	3.750	7.500	5.250	8.500	5.750
F2	6.500	2.125	6.500	2.875	7.875	4.000	8.125	4.750
F3	6.000	2.875	4.250	1.625	7.625	4.500	6.125	3.000
F4	4.750	5.250	5.000	6.500	6.750	7.250	7.000	8.125
F5	4.125	5.250	5.000	5.000	6.000	7.000	7.000	6.875
F6	4.000	5.500	5.250	4.250	6.000	7.500	6.875	6.125
F7	4.750	3.500	3.000	3.875	6.625	5.500	5.000	5.750
F8	4.750	3.250	3.500	3.500	6.625	5.250	5.500	5.500
F9	3.375	5.500	2.875	6.000	5.250	7.500	4.750	7.875
F10	3.750	6.750	4.500	7.000	5.750	8.375	6.500	8.375
F11	4.500	5.750	5.250	3.875	6.375	7.625	7.250	5.750
F12	3.625	5.000	3.375	7.000	5.500	6.875	5.125	8.500
F13	2.000	4.000	3.250	4.000	4.000	6.000	5.250	6.000
F14	3.000	7.250	1.500	5.500	5.000	8.625	2.750	7.125
F15	1.500	3.500	3.000	2.875	3.000	5.500	5.000	4.750
F16	2.250	2.250	4.250	4.000	3.750	3.750	6.000	6.000
F17	6.500	6.000	6.250	6.000	8.250	7.750	7.875	7.875
F18	1.750	3.375	3.500	5.250	3.250	5.000	5.500	7.125

Italics indicate the weight of the risk factors.

shows an assessment matrix of the average score of the eight experts’ comprehensive consideration of importance. The information of the data collected by the eight experts for ranking risks is described by Excel Table in Figure A1.

Based on the evaluation of severity, probability of occurrence, measurability, and expected cost, the GRA calculation steps are detailed through the EXCEL tool for ranking 18 failure modes, as shown in Figure A2. In addition, the results of the ranking failure modes are shown in

Table 9. Results of the GRA method for ranking 18 failure modes.

No.	Failure Modes	⊗Wi	Rank
F1	Overexertion	0.614	5
F2	Repetitive motion	0.560	11
F3	Bodily reaction	0.463	17
F4	Fall on same level	0.668	3
F5	Fall to lower level	0.594	6
F6	Struck by object	0.580	10
F7	Struck against object	0.487	14
F8	Struck by protrusion	0.485	15
F9	Object falling	0.594	7
F10	Wrapped/clamped	0.708	2
F11	Caught in or compressed by	0.587	8
F12	Highway incident	0.634	4
F13	Tool rebound/bump	0.488	13
F14	Electric shock	0.586	9
F15	Burn by high/low temperature	0.443	18
F16	Hazardous materials	0.477	16
F17	Unsafe distance	0.725	1
F18	Assault/violence	0.515	12

. The higher the grey value of Wi is, the higher the risk level of the fault mode. Therefore, the ranking result of each risk of picking and material-handling accidents can show that “F17” (unsafe distance) is the most critical failure mode, followed by “F10” (wrapped/clamped), “F4” (fall on same level), “F1” (overexertion), and “F12” (highway incident), as shown in Table 9. Thus, the grey value of Wi indicates that risk managers should give priority to formulating improvement strategies based on these ranks.

4.4. Management Implications

The results of the top five fault modes are: “F17” (unsafe distance) > “F10” (wrapped/clamped) > “F4” (fall on same level) > “F12” (highway incident) > “F1” (overexertion). “F17” (unsafe distance) is the most important risk, and the main reason might be that the person cannot clearly recognize either the danger situation or his own work scope, according to the interviewee. For example, the crane driver asks you to help with hooks, lanyards, etc., and then you enter the unsafe range of the crane operation. Sometimes, you take the initiative to direct or help and enter the unsafe range but are not delegated to do it. In addition, “F10” (wrapped/clamped) is the top-2 important risk. To improve efficiency in the warehouse facility, the power equipment seems to be running faster and faster when it is processing some added-value activities. Therefore, the accidents of limb injury from both “F10” (wrapped/clamped) and “F12” (highway incident: top 4) appear to be more serious than they were in the past when accidents happened.

The accidents of “F4” (fall on same level) or “F1” (overexertion) appear to be important but often overlooked, and are the top 3 and 5 important risks, respectively, separately based on the ranks of crucial risk as shown in Table 9. The main reasons for the injuries being overlooked by people might be that they do not have serious influences on the physical and mental health of employees, but the total cost of accidents is surprisingly staggering. In fact, more than $600 billion in direct costs for worker compensation were spent on compensable injuries in the United States from 1998 to 2010, and the costs of worker compensation for “F1” (overexertion) and “F4” (fall on same level) account for 26.8% and 16.9%, respectively [2], which are also the top 2 causes of disabling injuries.

Risk mitigation is an issue that affects all stakeholders from board members to all employees. The empirical results of 18 critical risks of picking and material-handling accidents improve visibility compared with the past research study [24]. According to the literature review [2], the result of relative ranking seems to be consistent with the logistics industry risk accidents evaluated, or it is closely in line with the current industrial situation in Taiwan. The developed results of evaluating the risks of picking and material-handling accidents in a warehouse facility are, thus, able to create values for logistics risk mitigation in practice in Taiwan. Therefore, it is better to benchmark the significance, which combines to indicate the potential hazard areas, provide safety handbooks, use the right tools for the job, and maintain a safe working environment for accident prevention.

5. Discussions

A literature review of past studies shows that HFACS and FMEA had hardly been integrated to form a risk assessment [9]. However, it is one of the most significant studies of evaluating risk based on two main reasons. First, HFACS is very important analysis, which can be used to explore the potential risk of picking and material-handling accidents in warehouse facilities. In addition, FMEA is usually applied to evaluate risk factors and obtain the risk evaluation matrix. Therefore, an integrated analysis of HFACS and FMEA is a kind of comprehensive risk assessment and is a better mode for risk mitigation, which is applied by this paper to evaluate the risk of picking and material-handling accidents in warehouse facilities.

In addition, for calculating the weights of the evaluation criteria for solving MCDM problems, some methods have been utilized, such as stepwise weight assessment ratio analysis (SWARA), the analytic hierarchy process (AHP), the analytic network process (ANP), the full consistency method (FUCOM), criteria importance through inter-criteria correlation (CRITIC), entropy, level-based weight assessment (LBWA), and so on [28]. A literature review shows that the developed BWM was the first to overcome some shortcomings of the analytic hierarchy process (AHP) in 2015 [27]. For example, BWM only needs to have 2n-3 comparisons while AHP needs n(n-1)/2 comparisons. Usually, the decision-makers prefer to have a unique optimal solution, but the min–max model may result in multiple optimal solutions. Therefore, the authors amended the mathematical calculation based on the same philosophy, but yielded a unique solution in 2016 [16].

Furthermore, the interval-valued intuitionistic uncertain linguistic set (IVIULSs) is used to improve the best–worst method (BWM) in the alternative evaluation [19,30]. Not only can BWM be used to derive the weights independently, it can also be combined with other MCDM methods of simple additive weighting (SAW), the technique for order of preference by similarity to ideal solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), grey relational analysis (GRA), complex proportional assessment of alternatives (COPRAS), etc. [28].

In our real world, because of the actual system provides the message to the human being is not complete, mean it is under uncertainty grey. Hence, the article uses grey system theory as the core of mathematical to analyze the state. Since the invention of grey system theory in 1982, it has been a very important theory successfully applied in many fields and used more than three decades [17]. The essential contents and topics of the grey system theory encompass the following areas: grey relational space, grey generating space, grey forecasting, grey decision making, grey control, and grey mathematics [31]. The grey relational grade has been one of the very important chapters in the grey system theory, whose main function is to measure the norm of a discrete sequence.

A literature review of past studies, especially on the applications of GRA, shows that there are many scholars proposing different GRA models for resolving MCDM problems. Focusing on the comparisons with past related studies, five different GRA methods [17] are directly cited by this paper for ranking 18 failure modes based on Table 8 of the assessment matrix of the average score by the eight experts. The calculation steps are explained in Appendix B, and Equations (A1)–(A4) are used for ranking, as shown in Figure A3. The results of the five different methods include Deng’s GRA, Wu’s GRA, Wen’s GRA, Hsia’s GRA, and Nagai’s GRA [17], as shown in

Table 10. Results of the five different GRA methods.

Method	Deng’s GRA		Wu’s GRA		Wen’s GRA		Hsia’s GRA		Nagai’s GRA
⊗	Wi	Rank	Wi	Rank	Wi	Rank	Wi	Rank	Wi	Rank
F1	0.614	5	0.815	8	0.831	6	0.600	6	0.522	8
F2	0.560	11	0.743	11	0.757	11	0.369	11	0.267	11
F3	0.463	17	0.679	18	0.667	17	0.020	17	0.000	18
F4	0.668	3	0.926	2	0.927	3	0.845	3	0.832	2
F5	0.594	6	0.867	4	0.850	5	0.653	5	0.675	4
F6	0.580	10	0.844	5	0.829	8	0.595	8	0.609	5
F7	0.487	14	0.741	12	0.718	13	0.229	13	0.263	12
F8	0.485	15	0.740	13	0.716	15	0.223	15	0.258	13
F9	0.594	7	0.808	9	0.818	9	0.562	9	0.497	9
F10	0.708	2	0.924	3	0.953	2	0.903	2	0.826	3
F11	0.587	8	0.839	6	0.831	7	0.600	7	0.594	6
F12	0.634	4	0.833	7	0.853	4	0.662	4	0.577	7
F13	0.488	13	0.739	14	0.717	14	0.226	14	0.253	14
F14	0.586	9	0.738	15	0.770	10	0.413	10	0.248	15
F15	0.443	18	0.687	17	0.662	18	0.000	18	0.038	17
F16	0.477	16	0.719	16	0.700	16	0.158	16	0.173	16
F17	0.725	1	1.000	1	1.000	1	1.000	1	1.000	1
F18	0.515	12	0.751	10	0.740	12	0.310	12	0.299	10

and Figure 1.

In the context of evaluation or selection, different GRA methods might generate different sorting results for the alternatives. In addition, as the number of criteria or alternatives in the problem increases, the ranking results obtained with the different MCDM methods become increasingly inconsistent [9]. Therefore, in 2020, a novel model of integrating multiple MADM methods was proposed. The paper [30] suggests that the performance calculation technique of the integrated multiple multi-criteria decision-making (PCIM−MCDM) is an appropriate integration method and is essential to determine the final utility degree for each alternative. In their study of evaluating risk factors, the results obtained by four MCDM methods are integrated into a final ranking index for evaluating critical failure modes in manufacturing, which include four methods of SAW, VIKOR, GRA, and COPRAS. In addition, the proposed integrated model is a better method and can help risk managers make more comprehensive decisions in the ranking of failure modes [9].

Therefore, the PCIM−MCDM [9] calculation steps of the mathematical equations are directly cited by this paper for ranking 18 failure modes, which are explained in Appendix C, and Equations (A5)–(A7) are used for ranking, as shown in Figure A4. The PCIM−GRA method determines the failure mode ranking using five GRA methods, which can be used to overcome the shortcomings of conventional FMEA in the practical applicability [9]. The results of the PCIM−GRA method for ranking 18 failure modes are shown in

Table 11. Results of the PCIM−GRA method for ranking 18 failure modes.

No.	${\mathit{a}}_{\mathit{h}}^{+}$	${\mathit{a}}_{\mathit{h}}^{-}$	FRIh	⊗ Wi	Rank
F1	0.681	0.842	0.024	0.192	8
F2	1.042	0.484	−0.029	−0.236	11
F3	1.498	0.028	−0.097	−0.780	18
F4	0.257	1.261	0.086	0.695	3
F5	0.532	0.988	0.046	0.368	4
F6	0.625	0.894	0.032	0.256	6
F7	1.158	0.361	−0.047	−0.379	13
F8	1.166	0.353	−0.048	−0.388	14
F9	0.729	0.792	0.017	0.133	9
F10	0.219	1.309	0.092	0.747	2
F11	0.631	0.888	0.031	0.249	7
F12	0.592	0.932	0.037	0.299	5
F13	1.167	0.352	−0.048	−0.390	15
F14	1.025	0.517	−0.025	−0.206	10
F15	1.489	0.039	−0.095	−0.768	17
F16	1.275	0.242	−0.064	−0.520	16
F17	0.000	1.515	0.124	1.000	1
F18	1.068	0.450	−0.034	−0.273	12
	15.154	12.246	0.124

and Figure 2, by which it can be seen that F17 is the most critical failure mode, followed by F10 > F4 > F5 > F12. The sum of their weights exceeds 0.385 (FRI_h: 0.124 + 0.092 + 0.086 + 0.046 + 0.037 = 0.385), indicating that these criteria have a high degree of influence on the overall evaluation model. The risk evaluation process is difficult and complicated. The PCIM−GRA is a better solution to this risk issue because it can simplify the analytical process, provide results that meet the decision-makers’ expectations, and suggest improvement plans [9].

Due to the limitation of research time, this paper illustrates the applications of BWM and GRA to evaluate the risk of picking and material-handling accidents in warehouse facilities, which mainly focus on the PX Mart logistics center for normal- and low-temperature products in Taiwan; it is hence suggested that future research should focus on the issue of the different logistics industries, different logistics product lines, green logistics, or cold-chain logistics.

6. Conclusions

Accidents have become of wide concern to the public because they often cause heavy economic losses and heavy casualties. Due to trade liberalization, commodity flows are promoted and the relevant warehouse facilities have increased to enhance the capacities of logistics movement. However, because warehouse facilities are dangerous places to work, it is critical to foster the safety and reliability of warehouse facilities to reduce accidents. However, in the relevant literature, the increased safety of warehouse facilities has hardly been researched. This is a main research gap, so the authors would like to enhance warehouse facility reliability to help risk managers establish properly risk mitigation strategies of picking and material-handling accidents in the warehouse facility to reduce or avoid accidents.

First, collecting the critical risks, there are 18 critical risks of picking and material-handling accidents in the warehouse facility obtained after three discussions and revisions. Then, based on the HFACS model and FMEA approach, the four risk indicators of occurrence (O), severity (S), detection (D), and expected cost (E) are calculated by BWM for determining the weights of the indicators. The results show that the expected cost is the most important weighted indicator, as well as the expected cost > detection > severity > occurrence.

In addition, followed by application of the GRA method to obtain the priority for each failure mode, the higher the value of the weighted indicated is, the higher the risk level of the fault mode. The ranking result of each failure mode of picking and material-handling accidents can show that “F17” (unsafe distance) is the most critical failure mode, followed by “F10” (wrapped/clamped), “F4” (fall on same level), “F12” (highway incident), and “F1” (overexertion).

Furthermore, the result of relative ranking is closely in line with the current industrial situation of logistics. The developed results of evaluating the risks of picking and material-handling accidents in warehouse facilities are, thus, able to create values for risk mitigation in practice. The higher weighted value indicates that risk managers should give priority to formulating improvement strategies based on these ranks.

Finally, the main contributions of industrial importance are summarized as follows:

• An integrated analysis of HFACS and FMEA suggested by this paper is a better mode with risk mitigation in practice.
• A grey interval number of BWM to obtain standard weights is used to improve the consistency of evaluation, which helps decision-makers clearly understand the importance of each risk indicator.
• An interval number of GRA to obtain ranks is also used to improve the shortcomings of information uncertainty. Therefore, decision-makers are more aware of the importance, so as to be able to properly improve risks in different practical applications, according to the different product lines or different logistics industries.
• A proposed suggestion of 18 critical risks of picking and material-handling accidents identified can be used to greatly reduce/avoid human casualties and monetary losses separately. It also makes up for the insufficiency of past research that lacks an empirical analysis of the risks of picking and material-handling accidents in warehouse facilities.